Multicore ring fibers and quantum systems comprising such fibers

ABSTRACT

A multicore optical fiber that includes a plurality of waveguiding cores disposed in a cladding. The plurality of cores are situated adjacent to at least one other core with a core center to core center spacing being not larger than 10 times the radius of the average core, such that the greater than 10% of the light will couple from one core to the adjacent core over a propagating distance of 1 cm, along the fiber length so as to provide coupling between the adjacent cores and to enable quantum walk. The plurality waveguiding cores are disposed in the cladding in a ring distribution or at least a portion of the ring distribution.

CROSS-REFERENCE OF RELATED APPLICATIONS

This application claims the benefit of priority under 35 U.S.C. § 119 ofU.S. Provisional Application Ser. No. 62/912,426 filed on Oct. 8, 2019,and U.S. Provisional Application Ser. No. 62/912,414 filed on Oct. 8,2019, the content of which is relied upon and incorporated herein byreference in its entirety.

BACKGROUND

The present disclosure relates to multicore optical fibers suitable foruse in quantum systems and to systems comprising such multicore opticalfibers. More specifically, the present disclosure relates systemscomprising multicore ring fibers, for example multicore ring fibers withcores arranged in a periodic or a non-periodic sequence for realizinglocalized quantum walks The cores have center to core center spacingbeing not larger than 10 times the radius of the average core, such thatthe greater than 10% of the light will couple from one core to theadjacent core over a propagating distance of at least 1 cm, to enablequantum walk.

SUMMARY

According to one embodiment of the present disclosure, a multicoreoptical fiber includes a plurality of fiber cores disposed in a fibercladding. The plurality of waveguiding cores disposed in a cladding, andare situated adjacent to at least one other core with a core center tocore center spacing being not larger than 10 times the radius of theaverage core, such that the greater than 10% of the light will couplefrom one core to the adjacent core over a propagating distance of 1 cm,along the fiber length so as to provide coupling between the adjacentcores and to enable quantum walk; and the plurality waveguiding coresare disposed in the cladding in a ring distribution or at least aportion of the ring distribution

A multicore optical fiber comprising:

-   -   a cladding,    -   a plurality of cores disposed in a cladding, wherein:        -   the plurality of cores comprise one or more first            waveguiding cores and one or more second waveguiding cores,            wherein said cores are situated adjacent to at least one            other core with a core center to core center spacing being            not larger than 10 times the radius of the average core,            such that the greater than 10% of the light will couple from            one core to the adjacent core over a propagating distance of            1 cm, along the fiber length so as to provide coupling            between the adjacent cores and to enable continuous quantum            walk;        -   the one or more first waveguiding cores comprise a first            propagation constant, the one or more second waveguiding            cores comprise a second propagation constant, and the first            propagation constant is different than the second            propagation constant; and            the one or more first waveguiding cores and the one or more            second waveguiding cores are disposed in the cladding in a            ring distribution and at least a portion of the ring            distribution is arranged based on a non-periodic or a            quasi-periodic sequence

According to one embodiment a multicore optical fiber comprises:

-   -   a cladding,    -   a plurality of cores disposed in a cladding, wherein:        -   the plurality of cores comprise one or more first            waveguiding cores and one or more second waveguiding cores,            wherein said cores are situated adjacent to at least one            other core with a core center to core center spacing being            not larger than 10 times the radius of the average core, so            as to provide coupling between the adjacent cores to enable            continuous quantum walk, such that the greater than 10% of            the light will couple from one core to the adjacent core            over a propagating distance of 1 cm, along the fiber length;        -   the one or more first waveguiding cores comprise a first            propagation constant, the one or more second waveguiding            cores comprise a second propagation constant; and            the one or more first waveguiding cores and the one or more            second waveguiding cores are disposed in the cladding in a            ring distribution and at least a portion of the ring            distribution is arranged based on a periodic sequence.

Although the concepts of the present disclosure are described hereinwith primary reference to quantum walks, it is contemplated that theconcepts will enjoy applicability to any quantum systems, for example:quantum information system, quantum communication system, quantumcomputing system, and quantum simulations.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

The following detailed description of specific embodiments of thepresent disclosure can be best understood when read in conjunction withthe following drawings, where like structure is indicated with likereference numerals and in which:

The following detailed description of specific embodiments of thepresent disclosure can be best understood when read in conjunction withthe following drawings, where like structure is indicated with likereference numerals and in which:

FIG. 1 schematically depicts a communications system including a photongenerator, a multicore optical fiber, and a photon detector, accordingto one or more embodiments shown and described herein;

FIGS. 2 and 2A schematically depicts a cross-section of exemplarymulticore optical fiber, according to one or more embodiments shown anddescribed herein;

FIG. 2B schematically depicts a cross-section of another examplemulticore optical fiber, according to one or more embodiments shown anddescribed herein;

FIG. 2C schematically depicts a cross-section of another examplemulticore optical fiber, according to one or more embodiments shown anddescribed herein;

FIG. 3A schematically depicts a cross-section of an an example multicoreoptical fiber;

FIG. 3B depicts an image of a cross-section of a manufactured multicoreoptical fiber corresponding to FIG. 3A;

FIG. 3C graphically depicts measured photon probability distributiondetermined using a communications system comprising the fiber of FIG.3B, according to one or more embodiments shown and described herein.

FIG. 3D graphically depicts modelled photon probability distributiondetermined using a communications system, according to one or moreembodiments shown and described herein that utilizes multicore opticalfiber of FIG. 3B;

FIG. 4A schematically depicts a cross-section of another examplemulticore optical fiber, according to one or more embodiments shown anddescribed herein;

FIG. 4C graphically depicts measured photon probability distributiondetermined using a communications system comprising the fiber of FIG.4A, according to one or more embodiments shown and described herein;

FIG. 4B depicts an image of a cross-section a manufactured multicoreoptical fiber corresponding to the fiber FIG. 4A;

FIG. 4C graphically depicts measured photon probability distributiondetermined using a communications system comprising the fiber of FIG.4B, according to one or more embodiments shown and described herein;

FIG. 4D graphically depicts modelled photon probability distributiondetermined using a communications system comprising the fiber of FIG.3A, according to one or more embodiments shown and described herein;

FIG. 5 illustrates the general rule for recursive construction ofquasi-periodic array of waveguiding cores;

FIG. 6 illustrates a construction of an exemplary Fibonacci arraysequence of waveguiding cores (FAWC);

FIG. 7A illustrates construction of the core ring distribution in 4^(th)order Fibonacci multicore ring fiber (FMCRF4);

FIG. 7B illustrate construction of the core ring distribution in 5^(th)order Fibonacci multicore ring fiber (FMCRF5);

FIG. 7C illustrate construction of the core ring distribution in 6^(th)order Fibonacci multicore ring fiber (FMCRF6);

FIGS. 8A-8C illustrate simulation results of probability distribution ofphotons in quantum walks in multicore optical fibers with a core ringdistribution, where the core comprises 15 waveguiding cores, 23waveguiding cores and waveguiding 39 cores, respectively.

FIG. 8D illustrates simulation results of probability distribution ofphotons in quantum walks in a system comprising 4^(th) order Fibonaccimulticore ring fiber (FMCRF4) with 15 waveguiding cores;

FIG. 8E illustrates simulation results of probability distribution ofphotons in quantum walks in a system comprising 5^(th) order Fibonaccimulticore ring fiber (FMCRF5) with 23 cores;

FIG. 8F illustrates simulation results of probability distribution ofphotons in quantum walks in a system comprising 6^(th) order Fibonaccimulticore ring fiber (FMCRF6) with 39 cores;

FIG. 9 illustrates schematically a system including a photon generator(source), a multicore optical fiber, and a photon detector, according toone or more embodiments shown and described herein;

FIG. 10 illustrates an exemplary image provided by an of algorithm fordetecting location of the waveguiding cores, according to one or moreembodiments shown and described herein.

DETAILED DESCRIPTION

Quantum walks have a variety of potential applications in quantumcommunications and quantum computing, for example, in the development ofquantum algorithms and quantum simulations. Quantum walks may increasecomputing speed and facilitate problem solving that is not feasibleusing a classical computer. In addition, photons are useful forperforming a quantum walk due to the dual wave-particle nature ofphotons. One phenomenon that occurs in a quantum walk is localization,which is the absence of diffusion of waves in a disordered medium.Localized quantum walks may result in symmetrical probabilitydistributions and thus localized quantum walks show potential forapplications in quantum communication, for example, using localizedphotonic states for the secure transmission of information and usinglocalized photonic states as a quantum memory. Localized quantum walksmay be realized using randomly disordered systems of waveguides (e.g.,spatially or temporally disordered), but this requires a large number ofrandom disorder systems and the randomness of each system needs to becontrolled within a defined range of the disorder. Further, localizedquantum walks that result in symmetrical probability distributions areimpossible in spatially random disorder systems and while localizedquantum walks with symmetrical probability distribution are possiblewith temporally random disorder systems by using multiple quantum coins,the multiple quantum coin approach is difficult to implementpractically. Thus, improved methods and systems for realizing localizedquantum walks are desired.

Reference will now be made in detail to embodiments of a communicationssystem for realizing improved localized quantum walks. Thecommunications system includes a multicore optical fiber comprising acladding and a plurality of cores (also referred to herein as thewaveguiding cores) comprising one or more first waveguiding cores andone or more second waveguiding cores disposed in the cladding. The oneor more first waveguiding cores and one or more second waveguiding corescomprise differing propagation constants and are arranged in aquasi-periodic sequence. (The propagation constant of a mode in awaveguiding fiber core determines how the amplitude and phase of thatlight with a given frequency varies along the propagation direction z(i.e., along the core axis). A single mode fiber core has only one modepropagating through the core. The propagation constant depends on thewavelength of the light propagating through the waveguiding core.) Asused herein, a “quasi-periodic sequence” refers to a sequence arrangedwith a designed pattern that lacks translational symmetry. In addition,a structure (such as the multicore optical fiber) that is made using aquasi-periodic sequence is made using building blocks (e.g., arrangementsegments of waveguiding cores) that are arranged using a designedpattern that lacks translational symmetry. The quasi-periodic sequenceof first and second waveguiding cores forms a deterministic disordersystem and thus quantum walks performed by directing one or more photonsinto one or more waveguiding cores of the multicore optical fiber arelocalized and result in a symmetrical probability distribution that ispredictable, controllable, and repeatable. While not intending to belimited by theory, localized quantum walks performed in a disorderedsystem, such as the communication system described herein, can be usedto store information regarding an initial state of qubits and thus maybe used as part of a secured quantum memory. Further, storage time of aquantum memory will be directly related to the number of implementablesteps of the quantum walk. Without localization, the size of theposition space required to store the information increases linearly withtime, making it challenging to store information for long durations.

In addition, the communications system 100 comprises one or more photongenerators 180 optically coupled to an input end 114 of at least one ofthe plurality of cores 110 and one or more photon detectors 190optically coupled to an output end 116 of at least one of the pluralityof cores 110. For example, in some embodiments, at least one photondetector of the one or more photon detectors 190 is optically coupled tothe output end 116 of the plurality of cores 110.

In operation, the communications system 100 may be used to perform aquantum walk, which may be used to determine a photon probabilitydistribution. For example, performing the quantum walk may comprisedirecting a plurality of photons generated using the photon generator180 into the input end 114 of one or more individual waveguiding core ofthe multicore optical fiber 101, receiving the plurality of photonsusing one or more photon detectors 190, and determining a photonprobability distribution based on the plurality of photons received bythe one or more photon detectors 190. As used herein, a “photonprobability distribution,” is a distribution function that representsthe probabilities of a photon that is directed into the input end 114 ofthe multicore optical fiber 101 exiting the output end 116 of eachindividual waveguiding core of the plurality of cores 110 of themulticore optical fiber 101.

Referring now to FIGS. 2, 2A-2C, 3A, 3B and 4A, 4B, adjacent waveguidingcores of the plurality of cores 110 disposed in the ring distribution140 are spaced apart from one another by a spacing distance D (corecenter to core center distance D). While not intending to be limited bytheory, during a quantum walk, each photon “walks” through the multicoreoptical fiber 101, moving between adjacent cores via evanescent couplingwhile propagating from the input end 114 of the multicore optical fiber101 to the output end 116 of the multicore optical fiber 101. Thus, thespacing distance D between adjacent cores is close enough for evanescentcoupling to occur, for example, the spacing distance D may compriseabout 40 μm or less, for example, about 30 microns or less, about 25 μmor less, about 20 μm or less, about 15 μm or less, about 10 μm or less,about 7.5 μm or less, or the like. For example, D may comprise about 30μm or less, for example, about 25 μm or less, about 20 μm or less, about15 μm or less, about 10 μm or less, about 5 μm or less, or the like.

Further, in some embodiments, adjacent cores of the plurality of cores110 may be uniformly spaced in the ring distribution 140. The spacingdistance D′ between the edges of the adjacent cores is also close enoughfor evanescent coupling to occur, for example, the spacing distance D′may be greater than about 2 μm about 30 μm or less, for example, about25 μm or less, about 20 μm or less, about 15 μm or less, about 10 μm orless, about 7.5 μm or less, or the like. In some embodiments thedistance D′ is 3 μm to 30 μm, and in some embodiments 5 μm to 30 μm.

Referring to FIGS. 2, 2A-2C, 4A and 4B, the plurality of cores mayinclude one or more first waveguiding cores 120 that comprise a firstpropagation constant and the one or more second waveguiding cores 130that comprise a second propagation constant. Without intending to belimited by theory, the propagation constant of a waveguiding coredetermines how the amplitude and phase of light propagating in the coreswith a given frequency varies along a propagation direction. In theseembodiments the first propagation constant is different than the secondpropagation constant. The propagation constant depends on a number offactors, such as the refractive index of the cores and the diameter ofthe cores. The propagation constant may be determined by the V-number V,where

${V = {\left( {2\pi\; a} \right)\left( \frac{NA}{\lambda} \right)}},{{NA} = \left( {n_{WG} - n_{CLAD}} \right)^{\frac{1}{2}}},n_{WG}$is the refractive index of an individual cores of the plurality of cores110, n_(CLAD) is the refractive index of the cladding 105, α₁ is aradius of an individual cores of the plurality of cores 110, and λ isthe wavelength of one or more photons propagating along the plurality ofcores 110. The wavelength λ may be situated for example, in thefollowing wavelength ranges: 800 nm to 900 nm, 920 nm to 970 nm, or 1200nm to 1400 nm, 1530 nm to 1565 nm, or 1.0 μm to 1.1 μm.

Further, the one or more first waveguiding cores 120 comprise a firstV-number V₁, the one or more second waveguiding cores 130 comprise asecond V-number V₂, and the first V-number V₁ is different than thesecond V-number V₂. In particular, the first V-number

${V_{1} = {\left( {2\pi\; a_{1}} \right)\left( \frac{{NA}_{1}}{\lambda} \right)}},$where

${{NA}_{1} = \left( {n_{{WG}\; 1} - n_{CLAD}} \right)^{\frac{1}{2}}},n_{{WG}\; 1}$is the refractive index of the one or more first waveguiding cores 120,n_(CLAD) is the refractive index of the cladding 105, α₁ is a radius ofthe one or more first waveguiding cores 120, and A is the wavelength ofone or more photons propagating along the plurality of cores 110 and thesecond V-number

$V_{2} = {\left( {2\pi\; a_{2}} \right)\left( \frac{{NA}_{2}}{\lambda} \right)}$where

${{NA}_{1} = \left( {n_{{WG}\; 1} - n_{CLAD}} \right)^{\frac{1}{2}}},$n_(WG2) is the refractive index of the one or more second waveguidingcores 130, n_(CLAD) is the refractive index of the cladding 105, α₂ is aradius of the one or more second waveguiding cores 130, and λ is thewavelength of one or more photons propagating along the plurality ofcores 110. Moreover, as the one or more first waveguiding cores 120 andthe one or more second waveguiding cores 130 are single mode cores, thefirst V-number V₁ and the second V-number V₂ are less than 2.405.

As shown mathematically by the V-number, two waveguiding cores thatcomprise different refractive indices may comprise different propagationconstants and two waveguiding core that comprise different diameters maycomprise different propagation constants. For example, the one or morefirst waveguiding cores 120 comprise a first diameter and a firstrefractive index and the one or more second waveguiding cores 130comprise a second diameter and a second refractive index. To achievediffering propagation constants, the first diameter may be differentthan the second diameter, the first refractive index may be differentthan the second refractive index, or both.

Moreover, while not intending to be limited by theory, fields of thewaves (e.g., light waves) propagating in the multicore optical fiber 101of first and second waveguiding cores 120, 130 may be coupled and themulticore optical fiber 101 may comprise a first coupling coefficientκ₁₂ (i.e. the coupling coefficient for coupling from a secondwaveguiding core 130 to a first waveguiding core 120) and a secondcoupling coefficient κ₂₁ (i.e., the coupling coefficient for couplingfrom a first waveguiding core 120 to a second waveguiding core 130),which represent the amount of couplings between the fields in the twocores. In other words, coupling coefficients measure the amount ofoverlap between the modal fields ψ₁(x, y) and ψ₂(x, y) in a firstwaveguiding core 120 and a second waveguiding core 130, respectively.Thus, each coupling coefficient κ is governed by an overlap integral,which indicates the behavior of the coupling between the modal fieldsresulting in a transfer of energy from one waveguiding core to theother. Further, the first coupling coefficient κ₁₂ is different than thesecond coupling coefficient κ₂₁. In general, the modal fields inwaveguiding cores ψ₁(x, y) and ψ₂(x, y) depend on various parameterssuch as the widths (e.g., diameters) of the cores, the refractiveindices of the core s n₁(x, y), n₂(x, y), the material of the cladding105, and the wavelength of operation (λ). While not intending to belimited by theory, the coupling coefficients κ₁₂ and κ₂₁ may bemathematically represented by

$\kappa_{12} = {{\frac{k_{0}^{2}}{2\beta_{1}}\frac{\int{\int_{- \infty}^{\infty}{\psi_{1}^{*}\Delta\; n_{1}^{2}\psi_{2}{dxdy}}}}{\int{\int_{- \infty}^{\infty}{\psi_{1}^{*}\psi_{1}{dxdy}}}}\mspace{14mu}{and}\mspace{14mu}\kappa_{21}} = {\frac{k_{0}^{2}}{2\beta_{2}}\frac{\int{\int_{- \infty}^{\infty}{\psi_{2}^{*}\Delta\; n_{2}^{2}\psi_{1}{dxdy}}}}{\int{\int_{- \infty}^{\infty}{\psi_{2}^{*}\psi_{2}{dxdy}}}}}}$where b₁ is the propagation constant of the first waveguiding core 120,b₂ is the propagation constant of the second waveguiding core 130,

${k_{0} = \frac{2\pi}{\lambda}},{{\Delta\; n_{1}^{2}} = {n_{T}^{2} - n_{2}^{2}}},$and Δn₂ ²=n_(T) ²−n₁ ², and where n_(T)(x, y) is the index profile of atwo waveguiding core portion of the multicore optical fiber 101 thatcomprises an individual first waveguiding core 120 adjacent anindividual second waveguiding core 130.

Referring still to FIGS. 2, 2A-2C and 4A, 4B, in some embodiments atleast a portion of the ring distribution 140 is arranged based on aquasi-periodic sequence of the one or more first waveguiding cores 120and the one or more second waveguiding cores 130. In other words, thering distribution 140 is arranged such that the first and secondpropagation constants vary quasi-periodically and as such, the ringdistribution 140 is disordered, varying coupling coefficientsquasi-periodically also causes disorder.

The quasi-periodic sequence comprises a plurality of sequence segments.Each sequence segment is determined based on a quasi-periodic functionand comprises an order (e.g., an order of the quasi-periodic sequence,such as a first order, second order, third order, or the like). Further,each sequence segment corresponds to an arrangement segment 145 of oneor more first waveguiding cores 120, one or more second waveguidingcores 130, or a combination thereof. Each arrangement segment 145 maycomprise a single waveguiding core or may comprise multiple waveguidingcores. For example, in the embodiments depicted in FIGS. 2, 2A-2C and4A, 4B, the ring distribution 140 comprises arrangement segments 145that correspond with six orders of sequence segments, i.e., afirst-order arrangement segment 145 a, a second-order arrangementsegment 145 b, a third-order arrangement segment 145 c, a fourth-orderarrangement segment 145 d, a fifth-order arrangement segment 145 e, anda sixth-order arrangement segment 145 f. However, it should beunderstood that other ring distributions 140 are contemplated. Forexample, the ring distribution 140 may comprise a portion that follows aquasi-periodic sequence and another portion that does not. In addition,the portion of the ring distribution 140 that follows a quasi-periodicsequence may comprise any one or more sequence segments of aquasi-periodic sequence, not just the initial sequence segments of thequasi-periodic sequence. Example quasi-periodic sequences include theFibonacci sequence, the Thue-Morse sequence, and the Rudin-Shapirosequence. It should be noted that the example ring distributions 140depicted in FIGS. 2A-2B follow the Fibonacci sequence, but other ringdistributions are contemplated.

When the quasi-periodic sequence is a Fibonacci sequence, thequasi-periodic function of the Fibonacci sequence comprisesS_(N+1)=S_(N−1)S_(N), where S_(N) comprises an N-order sequence segmentand corresponds to an N-order arrangement segment. S₁=A, where Acomprises a first-order sequence segment and corresponds to afirst-order arrangement segment 145 a comprising an individual firstwaveguiding core 120 and S₂=B, where B comprises a second-order sequencesegment and corresponds to a second-order arrangement segment 145 bcomprising an individual second waveguiding core 130. S₃=S₁S₂=AB, whereAB comprises a third-order sequence segment and corresponds to athird-order arrangement segment 145 c comprising the first-orderarrangement segment 145 a adjacent the second-order arrangement segment145 b. In particular, the third-order arrangement segment 145 ccomprises an individual first waveguiding core 120 disposed directlyadjacent an individual second waveguiding core 130. S₄=S₂S₃=BAB, whereBAB comprises the fourth-order sequence segment and corresponds to afourth-order arrangement segment 145 d comprising the second-orderarrangement segment 145 b adjacent the third-order arrangement segment145 c. In particular, the fourth-order arrangement segment 145 d segmentcomprises an individual first waveguiding core 120 disposed directlybetween two individual second waveguiding cores 130. S₅=S₃S₄=ABBAB,where ABBAB comprises the fifth-order sequence segment and correspondsto a fifth-order arrangement segment 145 e comprising the third-orderarrangement segment 145 c adjacent the fourth-order arrangement segment145 d. Furthermore, S₆=S₄S₅=BAB, where BABABBAB comprises thesixth-order sequence segment and corresponds to a sixth-orderarrangement segment 145 f comprising the fourth-order arrangementsegment 145 d adjacent the fifth-order arrangement segment 145 e.

The Thue-Morse sequence is a binary sequence (an infinite sequence of 0sand 1s) obtained by starting with 0 and successively appending theBoolean complement of the sequence obtained thus far. The first fewsteps of this sequence yield the strings 0 then 01, 0110, 01101001,0110100110010110, and so on. The Boolean complement is the oppositedigit(s) in a binary system, for example the Boolean complement of 1 is0, the Boolean complement of 0 is 1, and the Boolean complement of 101is 010. When the quasi-periodic sequence is a Thue-Morse sequence, thequasi-periodic function of the Thue-Morse sequence comprisesT_(N+1)=T_(N) T_(N) , where T_(N) comprises a N-order sequence segmentand corresponds to an N-order arrangement segment 145 and T_(N)comprises a sequence segment of the Boolean complement of the T_(N)sequence segment and corresponds to the Boolean complement of theN-order arrangement segment 145.

In the Thue-Morse sequence, T₁=A, where A comprises a first-ordersequence segment and corresponds to a first-order arrangement segment145 a comprising an individual first waveguiding core 120. T₂=B, where Bcomprises a second-order sequence segment and corresponds to asecond-order arrangement segment 145 b comprising an individual secondwaveguiding core 130. T₃=T₂ T ₂=BA, where BA comprises a third-ordersequence segment and corresponds to a third-order arrangement segment145 c comprising the second-order arrangement segment 145 b adjacent theBoolean complement of the second-order arrangement segment 145 b. Inparticular, the third-order arrangement segment 145 c comprises anindividual second waveguiding core 130 directly adjacent an individualfirst waveguiding core 120. T₄=T₃ T ₃=BAAB, where BAAB comprises thefourth-order sequence segment and corresponds to a fourth-orderarrangement segment 145 d comprising the third-order arrangement segment145 c adjacent the Boolean complement of the third-order arrangementsegment 145 c. In particular, the fourth-order arrangement segment 145 dcomprises a pair of directly adjacent first waveguiding cores 120positioned directly between pair of second waveguiding cores 130. T₅=T₄T ₄=BAABABBA, where ABBAB comprises a fifth-order sequence segment andcorresponds to a fifth-order arrangement segment 145 e comprising thefourth-order arrangement segment 145 d adjacent the Boolean complementof the fourth-order arrangement segment 145 d. Further, T₆=T₅ T₅=BAABABBAABBABAAB, where BAABABBAABBABAAB comprises a sixth-ordersequence segment and corresponds to a sixth-order arrangement segment145 f comprising the fifth-order arrangement segment 145 e adjacent theBoolean complement of the fifth-order arrangement segment 145 e.

When the quasi-periodic sequence is a Rudin-Shapiro sequence, thequasi-periodic function of the Rudin-Shapiro sequence comprises afour-element substitution sequence with the following rules: P→PQ, Q→PR,R→SQ, and S→SR. Thus, a first-order sequence segment S₁=P, asecond-order sequence segment S₂=PQ, a third-order sequence segmentS₃=PQPR, a fourth-order sequence segment S₄=PQPRPQSQ, a fifth-ordersequence segment S₅=PQPRPQSQPRSRPR, and so on. Further, to obtain asequence of only two elements, A and B, the four-element sequence may bemapped onto a two element sequence where (P,Q)→A and (R,S)→B. Eachinstance of A corresponds to an individual first waveguiding core 120 ofan arrangement segment 145 and each instance of B corresponds to anindividual second waveguiding core 130 of an arrangement segment 145.Thus, S₁=A, where S₁ is a first-order sequence segment correspondingwith a first-order arrangement segment 145 a that comprises A, S₂=AA,where S₂ is a second-order sequence segment corresponding with asecond-order arrangement segment 145 b that comprises AA, S₃=AAAB, whereS₃ is a third-order sequence segment corresponding with a third-orderarrangement segment 145 c that comprises AAAB, S₄=AAABAABA, where S₄ isa fourth-order sequence segment corresponding with a fourth-orderarrangement segment 145 d that comprises AAABAABA, andS₅=AAABAABAABBBAB, where S₅ is a fifth-order sequence segmentcorresponding with a fifth-order arrangement segment 145 e thatcomprises AAABAABAABBBAB, and so on.

Referring now to FIG. 2, in some embodiments, the ring distribution 140of the one or more first waveguiding cores 120 and the one or moresecond waveguiding cores 130 comprises a quasi-periodic sequence inwhich the lowest order arrangement segment 145 is positioned on a firstside 111 of the multicore optical fiber 101 (e.g., the first-orderarrangement segment 145 a is positioned on the left side of themulticore optical fiber 101 in FIG. 2) and the highest order arrangementsegment is positioned on a second side 113 of the multicore opticalfiber 101, which is opposite the first side 111 (e.g., the sixth-orderarrangement segment 145 f is positioned on the right side of themulticore optical fiber 101 in FIG. 2). As depicted in FIG. 2A, thearrangement segments 145 of the ring distribution 140 may increasestepwise, in order, from the first side 111 to the second side 113(e.g., from the first-order arrangement segment 145 a on the left,stepwise to the sixth-order arrangement segment 145 f on the right).Moreover, while FIG. 2 depicts that the entire ring distribution 140comprises a quasi-periodic sequence extending in both the firstdirection 141 and the second direction 143, it should be understood thatthe entire ring distribution 140 or merely a portion of the ringdistribution 140 may comprise a quasi-periodic sequence. The first side111 and the second side 113 are not separated by a large distance D_(x)and accordingly the waveguiding cores adjacent to the sides 111 and 113couple to one another. That is, in this embodiment the distance D_(x) isrelatively small to enable evanescent coupling between the end cores,and a continuous quantum walk (QWs) within the core distribution 140.That is, multicore optical fiber configuration allows for an “endless”quantum walk—i.e., the photons walk around the ring without beingstopped by a physical boundary. This creates an open quantum system,which is useful in a simulation system (for example when simulatingmaterials with many nuclei). This embodiment can utilize a multicoreoptical fiber with fewer waveguiding cores, making it very efficient andless expensive to produce.

According to some embodiments a multicore optical fiber comprises:

-   -   a cladding,    -   a plurality of cores disposed in a cladding, wherein:        -   the plurality of cores comprise one or more first            waveguiding cores and one or more second waveguiding cores,            wherein said cores are situated adjacent to at least one            other core with a core center to core center spacing being            not larger than 10 times the radius of the average core,            such that the greater than 10% of the light will couple from            one core to the adjacent core over a propagating distance of            1 cm, along the fiber length so as to provide coupling            between the adjacent cores and to enable quantum walk            between the cores; and        -   the plurality of cores are disposed in the cladding in a            ring distribution.

According to some embodiments the distance Dx is equal or smaller thanthe distance D′. According to some embodiments the distance Dx<30 μm.

According to some embodiments a multicore optical fiber comprises:

-   -   a cladding,    -   a plurality of cores disposed in a cladding, wherein:        -   the plurality of cores comprise one or more first            waveguiding cores and one or more second waveguiding cores,            wherein said cores are situated adjacent to at least one            other core with a core center to core center spacing being            not larger than 10 times the radius of the average core,            such that the greater than 10% of the light will couple from            one core to the adjacent core over a propagating distance of            1 cm, along the fiber length so as to provide coupling            between the adjacent cores and to enable continuous quantum            walk;        -   the one or more first waveguiding cores comprise a first            propagation constant, the one or more second waveguiding            cores comprise a second propagation constant, and the first            propagation constant is different than the second            propagation constant;        -   the one or more first waveguiding cores and the one or more            second waveguiding cores are disposed in the cladding in a            ring distribution and at least a portion of the ring            distribution is arranged based on a non-periodic sequence.

According to some embodiments a spacing distance between each adjacentpair of waveguiding cores in the plurality of waveguiding cores is about30 μm or less. According to some embodiments the spacing distance Dbetween each adjacent pair of waveguides in the plurality of waveguidesis between 5 μm and 30 μm. According to some embodiments the spacingdistance D between each adjacent pair of waveguides in the plurality ofwaveguides is between 7.5 μm and 30 μm. According to some embodimentsthe spacing distance D between each adjacent pair of waveguides in theplurality of waveguides is between 10 μm and 30 μm. According to someembodiments, the waveguiding cores are step-index cores. According toother embodiments the waveguiding cores are graded index cores.According to some embodiments the spacing distance D′ between edges ofeach adjacent pair of waveguides in the plurality of waveguides isbetween 5 μm and 30 μm. According to some embodiments the spacingdistance D′ between edges of each adjacent pair of waveguides in theplurality of waveguides is between 7.5 μm and 30 μm. According to someembodiments the spacing distance D′ between the edges of each adjacentpair of waveguides in the plurality of waveguides is between 10 μm and30 μm. According to some embodiments, the waveguiding cores arestep-index cores. According to other embodiments the waveguiding coresare graded index cores.

According to some embodiments a multicore optical fiber comprises:

-   -   a cladding,    -   a plurality of cores disposed in a cladding, wherein:        -   the plurality of cores comprise one or more first            waveguiding cores and one or more second waveguiding cores,            wherein said cores are situated adjacent to at least one            other core with a core center to core center spacing being            not larger than 10 times the radius of the average core,            such that the greater than 10% of the light will couple from            one core to the adjacent core over a propagating distance of            1 cm, along the fiber length so as to provide coupling            between the adjacent cores and to enable quantum walk            between the cores;        -   the one or more first waveguiding cores comprise a first            propagation constant, the one or more second waveguiding            cores comprise a second propagation constant;        -   the one or more first waveguiding cores and the one or more            second waveguiding cores are disposed in the cladding in a            ring distribution.

According to some embodiments the one or more first waveguiding coresand the one or more second waveguiding cores have the differentdiameters. According to some embodiments the one or more firstwaveguiding cores and the one or more second waveguiding cores have thedifferent refractive index profiles. According to some embodiments theone or more first waveguiding cores and the one or more secondwaveguiding cores have the different refractive indices. According tosome embodiments the first propagation constant is different than thesecond propagation constant.

However, according to some embodiments the one or more first waveguidingcores and the one or more second waveguiding cores have the samediameter and the same refractive index, and the first propagationconstant and the second propagation constant are substantially the same.In these embodiments the core ring distribution is not quasi-periodic asshown in FIG. 2, but is instead periodic, as shown, for example in FIG.3A.

Referring now to FIG. 2A, in some embodiments, the ring distribution 140of the one or more first waveguiding cores 120 and the one or moresecond waveguiding cores 130 comprises a quasi-periodic sequence inwhich the lowest order arrangement segment 145 is positioned on a firstside 111 of the multicore optical fiber 101 (e.g., the first-orderarrangement segment 145 a is positioned on the left side of themulticore optical fiber 101 in FIG. 2A) and the highest orderarrangement segment is positioned on a second side 113 of the multicoreoptical fiber 101, which is opposite the first side 111 (e.g., thesixth-order arrangement segment 145 f is positioned on the right side ofthe multicore optical fiber 101 in FIG. 2A). As depicted in FIG. 2A, thearrangement segments 145 of the ring distribution 140 may increasestepwise, in order, from the first side 111 to the second side 113(e.g., from the first-order arrangement segment 145 a on the left,stepwise to the sixth-order arrangement segment 145 f on the right).Moreover, while FIG. 2A depicts that the entire ring distribution 140comprises a quasi-periodic sequence extending in both the firstdirection 141 and the second direction 143, it should be understood thatthe entire ring distribution 140 or merely a portion of the ringdistribution 140 may comprise a quasi-periodic sequence. The first side111 and the second side 113 are separated by a sufficient distance D_(x)such that the waveguiding cores adjacent to the sides 111 and 113 do notcouple to one another. In such embodiments it is preferable that D_(x)be greater than D′. According to some embodiments the distance Dx>30 μm.A system comprising such a fiber is a closed quantum system withboundary effects, and can simulate, for example when simulatingmaterials with multiple nuclei.

Referring now to FIG. 2B, in some embodiments, the plurality of cores110 comprise a central waveguiding core 112 that separates a firstsection 142 of the ring distribution 140 from a second section 144 ofthe ring distribution 140. The first section 142 of the ringdistribution 140 extends in a first direction 141 from the centralwaveguiding core 112 and comprises a quasi-periodic sequence of firstwaveguiding cores 120 and second waveguiding cores 130. The secondsection 144 of the ring distribution 140 extends in a second direction143 from the central waveguiding core 112 and comprises a quasi-periodicsequence of first waveguiding cores 120 and second waveguiding cores130. In some embodiments, the central waveguiding core 112 comprises thefirst-order arrangement segment 145 a for each of the quasi-periodicsequences that extend in both the first direction 141 and the seconddirection 143. The quasi-periodic sequences that extend in the firstdirection 141 and the second direction 143 may mirror one another. Forexample, in FIG. 2B, the quasi-periodic sequence extending both thefirst direction 141 and the second direction 143 comprises a Fibonaccisequence and include the first-order arrangement segment 145 a (i.e.,the shared central waveguiding core 112) through the sixth-orderarrangement segment 145 f. Moreover, while FIG. 2B depicts a pluralityof cores 110 that include the central waveguiding core 112 andquasi-periodic sequences extending in both the first direction 141 andthe second direction 143, it should be understood that the entire ringdistribution 140 or merely a portion of the ring distribution 140 maycomprise a quasi-periodic sequence.

Referring now to FIG. 2C, in some embodiments, the plurality of cores110 comprise a first central waveguiding core 112′ adjacent a secondcentral waveguiding core 112″. In the embodiment depicted in FIG. 2C,the ring distribution 140 extends in the first direction 141 from thefirst central waveguiding core 112′ and comprises a quasi-periodicsequence of first waveguiding cores 120 and second waveguiding cores130. In particular, the first central waveguiding core 112′ comprisesthe first-order arrangement segment 145 a of the quasi-periodic sequencethat extends in the first direction 141. Furthermore, the ringdistribution 140 extends in the second direction 143 from the secondcentral waveguiding core 112″ and comprises a quasi-periodic sequence offirst waveguiding cores 120 and second waveguiding cores 130. Inparticular, the second central waveguiding core 112″ comprises thefirst-order arrangement segment 145 a of the quasi-periodic sequencethat extends in the second direction 143. The quasi-periodic sequencesthat extend in the first direction 141 and the second direction 143 maymirror one another. For example, in FIG. 2C, the quasi-periodic sequenceextending both the first direction 141 and the second direction 143comprises a Fibonacci sequence and include the first-order arrangementsegment 145 a (i.e., the first central waveguiding core 112′ for thesequence extending in the first direction 141 and the second centralwaveguiding core 112″ for the sequence extending in the second direction143) through the sixth-order arrangement segment 145 f. Moreover, whileFIG. 2C depicts a plurality of cores 110 that include the first andsecond central waveguiding cores 112′, 112″ and quasi-periodic sequencesextending in both the first direction 141 and the second direction 143,it should be understood that the entire ring distribution 140 or merelya portion of the ring distribution 140 may comprise a quasi-periodicsequence.

Referring again to FIG. 2A-2C, it should be understood that the entirering distribution 140 or merely a portion of the ring distribution 140may comprise a quasi-periodic sequence. For example, the ringdistribution 140 may comprise adjacent arrangement segments 145corresponding with a first-order sequence segment through a second-ordersequence segment, a first-order sequence segment through a third-ordersequence segment, a first-order sequence segment through a fourth-ordersequence segment, a first-order sequence segment through a fifth-ordersequence segment, a first-order sequence segment through a sixth-ordersequence segment, a first-order sequence segment through a seventh-ordersequence segment, a first-order sequence segment through an eighth-ordersequence segment, and so on. Thus, it should be understood that the ringdistribution 140 may comprise any number of arrangement segmentscorresponding to any number of sequence segments. Further, in someembodiments, the ring distribution 140 comprises at least onearrangement segment 145 corresponding with a third-order sequencesegment or higher, a fourth-order sequence segment or higher,fifth-order sequence segment or higher, sixth-order sequence segment orhigher, seventh-order sequence segment or higher or the like. In someembodiments, the ring distribution 140 comprises arrangement segments145 corresponding with a third-order sequence segment and a fourth-ordersequence segment, a fourth-order sequence segment and a fifth-ordersequence segments, a third-order sequence segment through a fourth-ordersequence segment, or the like.

Multicore Optical Fiber

FIGS. 3A, 3B illustrates an example of a multicore ring optical fiber101 that comprises 39 cores situated within the cladding. The multicorering fiber shown in FIGS. 3A, 3B is designed and fabricated withidentical single mode (SM) waveguiding cores that are regularly periodicand a situated in a circular ring. In this exemplary fiber all of thecores are single mode cores and all cores have same Δn (relative tocladding) and the same core diameter d. That is, in this example fiberthe cores are designed to be identical. The main parameters of thismulticore optical fiber are: core diameter d=4.4 μm, index differenceΔn=ncore−nclad=0.0035, ring diameter r (i.e., distance r from each corecenter to the fiber center) is 120 μm, cladding diameter R is at least155 μm m (e.g., 160 μm to 500 μm), the waveguiding cores are regularly(periodically) placed in a ring formation with the same spacing betweenthe cores, and the input core in the central core CC. Measurement datashows that cores sizes are vary of about less than 10%, and average corediameter is 4.4 μm. FIG. 3B is a photograph of the manufactured fibercorresponding to FIG. 3A. FIG. 3C is a photograph of the manufactured ofFIG. 3B, with the light at the operating wavelength λ=1550 nmpropagating through the waveguiding cores. Other operating wavelengthsmay also be utilized. The operating wavelength λ may be situated forexample, in the following wavelength ranges: 800 nm to 900 nm, 920 nm to970 nm, or 1200 nm to 1400 nm, 1530 nm to 1565 nm, or 1.0 μm to 1.1 μm.

In our experiments of single-photon quantum walks (QWs), we launched thesignal into the center core (input core) of the core ring, and the QWsprocess takes place from the center waveguiding core (input waveguidingcore) to the end cores of the two symmetrical arms A1, A2. In thisembodiment, the two end-cores of the two arms A1, A2 are separated by alarger distance Dx than the rest of the cores in order to avoid couplingbetween these two end cores, so as not to provide continuous QWs on acontinuous curved core distribution 140. In such embodiments it ispreferable that D_(x) is greater than D′. For example, in someembodiments 2D′<D_(x)<10D′, or 2D′<D_(x)<30D′.

The spacing distance D′ between the edges of the adjacent waveguidingcores is also close enough for evanescent coupling to occur, forexample, the spacing distance D′ may be greater than about 2 μm about 30μm or less, for example, about 25 μm or less, about 20 μm or less, about15 μm or less, about 10 μm or less, about 7.5 μm or less, or the like.In some embodiments the distance D′ is 3 μm to 30 μm, and in someembodiments 5 μm to 30 μm.

According to some embodiments a multicore optical fiber comprises:

-   -   a cladding,    -   a plurality of cores disposed in a cladding, wherein:        -   the plurality of cores comprise one or more first            waveguiding cores and one or more second waveguiding cores,            wherein at least some of said cores are situated adjacent to            at least one other core with a core center to core center            spacing being not larger than 10 times the radius of the            average core, such that the greater than 10% of the light            will couple from one core to the adjacent core over a            propagating distance of 1 cm, along the fiber length so as            to provide coupling between the adjacent cores and to enable            quantum walk between the cores; and    -   the plurality of cores are situated periodically (or        substantially periodically) within in the ring distribution.

According to some embodiments the distance Dx is greater than thedistance D′. However, according to some embodiments the distance Dx isequal or smaller than the distance D′. According to some embodiments thedistance Dx>30 μm.

Calculated probability photon distribution of quantum walks in thismulticore optical fiber, and the of measured photon distribution(Experiment data) for this fiber are shown in FIGS. 3D and 3Crespectively. Both FIG. 3C and FIG. 3D show a typical pattern of quantumwalks, characterized by two strong lobes. That is, the experimentmeasurement of photon distribution at and simulation results are in goodagreement. The feature of quantum walks with two strong lobes at the endof walking length are clearly shown in both FIGS. 3C and 3D.

In some embodiments of periodically arranged core distributions thedistance Dx about the same as D′. In such embodiments the sides 111 and113 are close enough to enable coupling between the two end cores,providing continuous quantum walk between the waveguiding cores. Thus,according to some embodiments a multicore optical fiber comprises:

-   -   a cladding,    -   a plurality of cores disposed in a cladding, wherein:        -   the plurality of cores comprise one or more first            waveguiding cores and one or more second waveguiding cores,            wherein at least some of said cores are situated adjacent to            at least one other core with a core center to core center            spacing being not larger than 10 times the radius of the            average core, such that the greater than 10% of the light            will couple from one core to the adjacent core over a            propagating distance of 1 cm, along the fiber length so as            to provide coupling between the adjacent cores and to enable            quantum walk (e.g., continuous quantum) walk between the            waveguiding cores;        -   the one or more first waveguiding cores comprise a first            propagation constant, the one or more second waveguiding            cores comprise a second propagation constant, and the first            propagation constant is different than the second            propagation constant;        -   the one or more first waveguiding cores and the one or more            second waveguiding cores are disposed in the cladding in a            ring distribution.

According to some embodiments the minimum distance between the edges ofthe adjacent core is at least equal to half the radius of the smallercore (and preferably at least the radius of the core). According to someembodiments the one or more first waveguiding cores and the one or moresecond waveguiding cores have the same diameter and the same refractiveindex.

According to some embodiments a multicore optical fiber comprises:

-   -   a cladding,    -   a plurality of cores disposed in a cladding, wherein:        -   the plurality of cores comprise one or more first            waveguiding cores and one or more second waveguiding cores,            wherein said cores are situated adjacent to at least one            other core with a core center to core center spacing being            not larger than 10 times the radius of the average core,            such that the greater than 10% of the light will couple from            one core to the adjacent core over a propagating distance of            1 cm, along the fiber length so as to provide coupling            between the adjacent cores and to enable continuous quantum            walk;        -   the one or more first waveguiding cores comprise a first            propagation constant, the one or more second waveguiding            cores comprise a second propagation constant, and the first            propagation constant is different than the second            propagation constant;        -   the one or more first waveguiding cores and the one or more            second waveguiding cores are disposed in the cladding in a            ring distribution and at least a portion of the ring            distribution is arranged based on a non-periodic sequence.        -   In some embodiments the first propagation constant and the            second propagation constant are the same. However, in some            embodiments, the first propagation constant and the second            propagation constant are different. According to some            embodiments a spacing distance between each adjacent pair of            waveguiding cores in the plurality of waveguiding cores is            about 30 μm or less. According to some embodiments the            spacing distance D between each adjacent pair of waveguides            in the plurality of waveguides is between 5 μm and 30 μm.            According to some embodiments the spacing distance D between            each adjacent pair of waveguides in the plurality of            waveguides is between 7.5 μm and 30 μm. According to some            embodiments the spacing distance D between each adjacent            pair of waveguides in the plurality of waveguides is between            10 μm and 30 μm. According to some embodiments, the            waveguiding cores are step-index cores. According to other            embodiments the waveguiding cores are graded index cores.            According to some embodiments the spacing distance D′            between edges of each adjacent pair of waveguides in the            plurality of waveguides is between 5 μm and 30 μm. According            to some embodiments the spacing distance D′ between edges of            each adjacent pair of waveguides in the plurality of            waveguides is between 7.5 μm and 30 μm. According to some            embodiments the spacing distance D′ between the edges of            each adjacent pair of waveguides in the plurality of            waveguides is between 10 μm and 30 μm. According to some            embodiments, the waveguiding cores are step-index cores.            According to other embodiments the waveguiding cores are            graded index cores.

According to some embodiments a multicore optical fiber comprises:

-   -   a cladding,    -   a plurality of cores disposed in a cladding, wherein:        -   the plurality of cores comprise one or more first            waveguiding cores and one or more second waveguiding cores,            wherein said cores are situated adjacent to at least one            other core with a core center to core center spacing being            not larger than 10 times the radius of the average core, so            as to provide coupling between the adjacent cores to enable            continuous quantum walk, such that the greater than 10% of            the light will couple from one core to the adjacent core            over a propagating distance of 1 cm, along the fiber length;        -   the one or more first waveguiding cores comprise a first            propagation constant, the one or more second waveguiding            cores comprise a second propagation constant;        -   the one or more first waveguiding cores and the one or more            second waveguiding cores are disposed in the cladding in a            ring distribution and at least a portion of the ring            distribution is arranged based on a periodic sequence.

In some embodiments the first propagation constant and the secondpropagation constant are the same. However, in some embodiments, thefirst propagation constant and the second propagation constant aredifferent.

According to some embodiments a spacing distance between each adjacentpair of waveguiding cores in the plurality of waveguiding cores is about30 μm or less. According to some embodiments the spacing distance Dbetween the centers of each adjacent pair of waveguides in the pluralityof waveguides is between 10 μm and 30 μm. According to some embodimentsthe spacing distance D′ between the edges of each adjacent pair ofwaveguiding cores in the plurality of waveguiding cores is between 7.5μm and 30 μm, or between 10 μm and 30 μm. According to some embodiments,the waveguiding cores are step-index cores. According to otherembodiments the waveguiding cores are graded index cores.

Exemplary Embodiment of the Multicore Fiber 101

FIG. 4A illustrates a of the multicore optical fiber 101 that comprises39 waveguiding cores 110 situated within the cladding 105. Thewaveguiding cores 110 comprising one or more first waveguiding coresarranged in a ring (e.g., in a broken ring comprising a plurality ofarms, for example Arm1, and Arm2) forming a ring distribution 140. Morespecifically, it is preferable, as shown in this embodiment, that thecore centers are spaced from the fiber center by a distance r. In someembodiments core centers are spaced from the fiber center by a distanceDc=r±0.2 dc, for example, Dc=r±0.15 dc, where dc is the diameter of thewaveguiding core. In other embodiments the edges of the cores nearest tothe fiber center may be spaced from the fiber center by the distance r′.In other embodiments the edges of the cores nearest to the cladding'souter diameter center may be spaced from the fiber center by thedistance r″. In this exemplary embodiment, the ring distribution 140includes of the one or more first waveguiding cores 120 and the one ormore second waveguiding cores 130 arranged in a quasi-periodic sequence.FIG. 4B is a photograph of the manufactured fiber corresponding to FIG.4A.

In this embodiment, the ring of cores is constructed with Fibonaccisequence of the two types of single mode (SM) cores, i.e., cores A(waveguiding cores 120) and cores B (waveguiding cores 130). Fiber coresA (i.e., the waveguiding cores 120) have the refractive index differencehaving Δn1=ncore1−nclad, where Δn1 is the refractive index of thewaveguiding cores 120, and nclad is the refractive index of the claddingat the operating wavelength (e.g., λ=1550 nm). Fiber cores B (i.e., thewaveguiding cores 130) have the refractive index differenceΔn2=ncore2−nclad, where Δn2 is the refractive index of the waveguidingcores 130 at the operating wavelength (e.g., λ=1550 nm). In thisembodiment all waveguiding cores 110 have same diameters d. However, insome embodiments the core diameters may not be the same. In general, theconstruction of core-ring arrangement 140 is the same as the sequence asthat of the Fibonacci arrays of waveguiding cores, which is illustratedin FIG. 5). Parameters of this embodiment of the optical fiber 101 areas follows. For the second waveguiding cores 120 the refractive indexdifference (relative to the cladding) is Δn1=ncore1−nclad=0.0035. Insome exemplary embodiments 0.0025≤Δn1≤0.01. For the second waveguidingcores 120 the refractive index difference Δn2=ncore1−nclad=0.0045. Insome exemplary embodiments 0.0025≤Δn2<0.01. In some exemplaryembodiments 0.001≤|Δn2−Δn1|≤0.01. The ring diameter (i.e., the distancer from the core centers to the of the center of the fiber) is 120 μm,and the outer cladding diameter R is greater than 160 μm (e.g., 500 μm,300 μm, 250 μm, or therebetween). Although the fiber core diameters weredesigned to be the same, the core diameters in a manufactured opticalfiber 101 were slightly different. Fabricated fiber measurements showthat cores diameters vary by 15% or less (as compared to the averagecore diameter), with the average core diameter being 4.55 mm. Thus, inthis embodiment, the diameters of the waveguiding cores aresubstantially the same.

Calculated probability photon distribution of quantum walks in thismulticore optical fiber embodiment, and the of measured photondistribution (Experimental data) for this fiber embodiment are shown inFIGS. 4D and 4C, respectively. Both FIG. 4C and FIG. 4D show differentbehavior than that exhibited by the multicore ring fiber of FIGS. 3A,3B. Instead of the typical pattern of quantum walks, characterized bytwo strong lobes as shown in FIGS. 3C and 3D, figures FIG. 4C and FIG.4D display only one strong lobe. The atypical feature of quantum walkswith only one strong lobe at the end of walking length produced due toquasi-periodic core distributions within the multicore fiber 101 are aclearly shown in both FIGS. 4C and 4D. That is, the experimentmeasurement of photon distribution at and simulation results are in goodagreement.

FIG. 5 illustrates the general rule for recursive construction ofquasi-periodic array of waveguiding cores with Fibonacci sequence basedon two different waveguiding cores. The j^(th)-order Fibonacci elementis defined as S_(j)=S_(j-2)S_(j-1), S₁=A, S₂=B, where A and B are twodifferent single-mode waveguiding cores. The waveguiding cores A and Bplaced closely to one another to ensure evanescent coupling between thetwo adjacent waveguiding cores. More specifically, FIG. 5 illustrates anexemplary recursive construction of quasi-periodic array (sequence(s))of waveguiding cores with Fibonacci sequence in jth-order of twodifferent waveguiding cores A and B, and elements S₁, S₂ . . . S₆ ofFibonacci arrays of waveguiding cores 120, 130 composed by two types ofwaveguiding cores: single mode waveguiding cores A (smaller circles,corresponding to the waveguiding cores 120) and single mode waveguidingcores B (larger circles, corresponding to the waveguiding cores 130).

FIG. 6 illustrates a construction of an exemplary Fibonacci array(sequence) of waveguiding cores (FAWC). In order to increase thecomplexity of the arrays of waveguiding cores, or to make thewaveguiding core sequence less orderly, we define a new j^(th)-orderFibonacci array of waveguiding cores as F₁=S₁S₂ . . . S_(j) where S₁, S₂. . . S_(j) are Fibonacci elements corresponding to the optical fiber ofFIG. 4A above. FIG. 5 illustrates schematically an example of how the6^(th)-order Fibonacci arrays of waveguiding cores (FAWC6) can beconstructed. It is noted that the arrays of waveguiding cores may notneed to be linear, and may be arranged in the same sequence along butalong a curve—i.e., ring-type fashion, as described and shown herein,however the sequence(s) of fiber core arrangement when the waveguidingcores are arranged so as to forming ring distribution 140 will besimilar.

FIG. 6 is a diagram of 6^(th) order Fibonacci arrays of waveguidingcores (FAWC6) composed by two types of waveguiding cores 120, 130. Morespecifically the plurality of waveguiding cores in this embodimentcomprise single mode waveguiding cores A (smaller circles, correspondingto the waveguiding cores 120) and B (larger circles, corresponding tothe waveguiding cores 130).

FIGS. 7A and 7B illustrate construction of the core ring distribution140 in 4^(th) order Fibonacci multicore ring fiber 101 (FMCRF4) and5^(th)-order Fibonacci multicore ring fiber 101 (FMCRF5), respectively.The ring of cores is symmetrical with two arms each is constructed asdescribed in FIG. 6 above. FIG. 7C illustrates a cores ring distribution140 in 6^(th) order Fibonacci multicore ring fiber 101 (FMCRF6) thatcomprises 39 waveguiding cores.

It is clear from FIGS. 7A-7C that the core rings constructed withFibonacci sequences of two different SM (single mode) waveguiding coresA and B are on-diagonal quasi-periodic, due to the Fibonaccidistributions of propagation constants β_(A) and β_(B). (For example,when the waveguiding cores A and B correspond to the waveguiding cores120, 130, respectively, β_(A)=b₁ and β_(B)=b₂, where b₁ is thepropagation constant of the first waveguiding core 120, b₂ is thepropagation constant of the second waveguiding core 130.) The couplingcoefficients between the nearest waveguiding cores are the functions ofthe overlapping between the modes and the propagation constants of thesewaveguiding cores. Consequently, the coupling coefficients in themulticore ring fibers 101 (for example Fibonacci Multicore Ring Fibers(FMCRFs) disclosed herein) also have quasi-periodic—or deterministicallydisordered distribution. Therefore, FMCRFs advantageously provideplatforms having both on- and off-diagonal deterministic disorders forrealizing LQWs deterministically (e.g., both propagation constants andcoupling coefficients are quasi-periodic). That is, multicore ringfibers (MCRFs) shaving waveguiding cores situated in a ring distributionconstructed with a Fibonacci sequence with two different waveguidingcores result in both propagation constants and coupling coefficients arequasi-periodic or deterministically disordered distributions.

FIGS. 8A-8C illustrate simulation results of probability distribution ofphotons in quantum walks in multicore optical fibers with a core ringdistribution that is periodic (similar to that of fiber of FIG. 3A, butcomprising: a) 15 waveguiding cores (FIG. 8A), b) 23 cores (FIG. 8B),and c) 39 cores (FIG. 8C). More specifically, FIGS. 8A-8C show thatprobability distribution of QWs in periodic MCRF with photons spreadacross the lattice by coupling from one waveguiding core to the adjacentwaveguiding core in a pattern characterized by two strong lobes.

The results for optical fiber with the waveguiding cores arranged inring distribution that has a quasi-periodic sequence are structurallydifferent. For example, LQWs are clearly shown in quasi-periodicFibonacci multicore ring fibers (FMCRFs). Furthermore, symmetricaldistributions of LQWs in FMCRFs can be achieved due to the symmetry ofthe quasi-periodic ring of cores in FMCRFs. FIGS. 8D-8E illustratesimulation results of probability distribution of photons in quantumwalks in with Fibonacci multicore ring fibers 101 that have d) 15waveguiding cores (FMCRF4, see FIG. 8D), e) 23 waveguiding cores(FMCRF5, see FIG. 8E), and f) with 39 waveguiding cores (FMCRF6, seeFIG. 8F).

Note that quantum walks multicore fiber with a periodic core ringdistribution (e.g., fiber of FIG. 3A) have photons spread across thelattice by coupling from one waveguiding core to its neighboringwaveguiding core(s) in a pattern characterized by two strong lobes, asin normal quantum walks on a line. However, the results forquasi-periodic core ring multicore optical fibers 101 (e.g., Fibonaccimulticore ring fibers) are different: localized quantum walks areclearly demonstrated in Fibonacci multicore ring fibers. Furthermore,symmetrical distributions of LQWs in FMCRFs can be achieved due to thesymmetry of the quasi-periodic ring of cores, for example in FMCRFs.

Design of Multicore Ring Fibers (MCRFs)

The design of MCRFs with a periodic core ring distribution is shown, forexample, in FIG. 3A. In this multicore ring fiber all the single modewaveguiding cores are regularly placed in two identical arms of a ring,with central waveguiding core being an input core is for input signalcoupling. The fiber design shown in FIG. 3a has the following features:

-   -   1. Fiber cores (i.e., the waveguiding cores) have mode field        diameters (MFDs) close (e.g., within 10%) to that of single mode        fiber for easy coupling to the single mode input fiber.    -   2. If desired, two end-cores in two arms A1, A2 of core ring are        spaced far enough apart by a distance Dx, in order to avoid        coupling between the two end-cores that would distort        distribution of the normal quantum walks in line, which do not        have such interaction.    -   3. Fiber cladding should not too close core ring to avoid        reflection at the boundary between the cladding and fiber jacket        or air surrounding the cladding. The reflection is very small        but could cause some distortion if cladding is too thin and        close to the core ring.

The fiber design of the optical fibers 101 with the quasi-periodic corering distribution, for example FMCRFs (is be similar as that for MCFsdescribed above, but, the core ring distribution 140 of the fibershaving a plurality of cores are arranged in a ring distribution that isquasi-periodic, e g., ring distribution that is based on Fibonaccisequences, Rudin-Shapiro, or Thue-Morse sequence. The core ringdistribution 140 may is comprised of at least two arms (for example twosymmetrical arms A1, A2). For example, each arm of the core ringdistribution 140 may be constructed with Fibonacci sequences ofwaveguiding cores as described herein and shown, for example, in FIGS.2, 2A-C and 4A-4B, and 7.

Fabrication of MCRFs

One exemplary fabrication method of MCRFs (e.g. FMCRFs) includesfabricating cylindrical rods of cladding glass having a top (flat)surface, drilling bores in the direction orthogonal to the flat surface,and inserting continuous core canes into the bore holes, forming amulti-core preform, and then drawing multi-core preform into amulti-core fiber. Another exemplary fabrication method of MCRFs (e.g.,FMCRFs) includes fabricating a cladding glass preform with the elongatedholes capable of receiving core rods, inserting core canes into theholes, consolidating the cladding glass around the core rods, therebyforming a multi-core preform, and then drawing multi-core preform into amulti-core fiber. Other methods of forming the multicore fibers can alsobe utilized.

Set-Up and Measurement

The MCRF (both periodic and FMCRF) with 39 single mode cores werecharacterized using a cross-polarization microscopy. The microscopysystem is a Nikon, high magnification optical microscope with error of±0.5 μm. The average core diameter measured is ˜4.40 μm and 4.55 μm forMCF and FMCF respectively. The average distance from center-to-center ofneighboring cores is ˜16.89 μm and ˜16.80 μm for periodic MCRF (similarto that of FIG. 3A) and FMCRF respectively. The index observed fromcrossed-polarization indicate that the periodic MCF have identicalrefractive index for all of cores, whereas the FMCF have different corerefractive indices grouped as described in previous sections. The corering radius r is approximately ˜120 μm and fiber cladding outer radiusis approximately ˜158 μm.

Demonstration of quantum walks in MCRFs and FMCF were conducted with astripped fiber, at approximately 4-cm length. The fiber is placed on av-groove in an imaging system shown in FIG. 9. A tunable source from1510-1590 nm laser illuminates the multicore ring fiber 101 The stepstaken to identify the central (20^(th)) core and measured the quantumwalk distribution is as follows:

-   -   1.) Illuminate subsections of the fiber of interest (FOI) such        that waveguiding cores are illuminated.    -   2.) Combine illumination images to identify the position of each        waveguiding core using Matlab/Labview algorithms to identify        circular objects and, for example draw the circle around the        object as shown in FIG. 10. More specifically, FIG. 10        illustrates a sample image of algorithm detecting location of        each cores. Circles are drawn around each waveguiding core's        location.    -   3.) Extract position of the central core (20^(th) Core).    -   4.) Illuminate the central core by butt-coupling with an single        mode fiber that is mode-matched to the MCRF cores.    -   5.) Capture image of signals.    -   6.) Repeat steps 4-5 for wavelength sweep from 1530-1559 nm to        account for fiber length variations.    -   7.) Calculate the total intensity within the MFD of each        waveguiding core, for example by utilizing either a Matlab        algorithm or another applicable software.

Experimentally, we have demonstrated quantum walks in at least two typesof quantum systems: quantum systems that utilize ordered periodicallyarranged multiple waveguiding cores, quantum systems comprising orderedand quasi-periodic arrays of cores or deterministically disordered arrayof waveguiding cores. The ordered system, MCRF, showed distributions ofthat expected for a quantum walk distribution. On the hand, the FMCRF, aquasi-periodic or deterministically disordered system, showslocalization as predicted by our simulation. However, the system can befurther improved as the tolerance for misalignment, surface roughness,reflection by air/cladding interface is quite strong especially for theFMCRF. Misalignment, roughness, air/cladding interfaces may causedistortion and unwanted localization and interferences in the fiber.These issues can be resolved using index matching oil to reducereflection at the interface between cladding and air. To achieve ashort-length fiber with minimal roughness to the end faces from badcleaving or from unwanted back-reflection from flat end faces, wefabricated a housing unit for the fiber made of angled-ferrules and/orcanes filled completely or in part with index-matching oil andhigh-refractive index adhesive. The ferrules are polished at angle orflat depending on tolerance for back-reflection.

For the purposes of describing and defining the present inventivetechnology, it is noted that reference herein to a variable being a“function” of a parameter or another variable is not intended to denotethat the variable is exclusively a function of the listed parameter orvariable. Rather, reference herein to a variable that is a “function” ofa listed parameter is intended to be open ended such that the variablemay be a function of a single parameter or a plurality of parameters.

It is also noted that recitations herein of “at least one” component,element, etc., should not be used to create an inference that thealternative use of the articles “a” or “an” should be limited to asingle component, element, etc.

It is noted that recitations herein of a component of the presentdisclosure being “configured” in a particular way, to embody aparticular property, or function in a particular manner, are structuralrecitations, as opposed to recitations of intended use. Morespecifically, the references herein to the manner in which a componentis “configured” denotes an existing physical condition of the componentand, as such, is to be taken as a definite recitation of the structuralcharacteristics of the component.

For the purposes of describing and defining the present inventivetechnology it is noted that the terms “substantially” and “about” areutilized herein to represent the inherent degree of uncertainty that maybe attributed to any quantitative comparison, value, measurement, orother representation. The terms “substantially” and “about” are alsoutilized herein to represent the degree by which a quantitativerepresentation may vary from a stated reference without resulting in achange in the basic function of the subject matter at issue.

Having described the subject matter of the present disclosure in detailand by reference to specific embodiments thereof, it is noted that thevarious details disclosed herein should not be taken to imply that thesedetails relate to elements that are essential components of the variousembodiments described herein, even in cases where a particular elementis illustrated in each of the drawings that accompany the presentdescription. Further, it will be apparent that modifications andvariations are possible without departing from the scope of the presentdisclosure, including, but not limited to, embodiments defined in theappended claims. More specifically, although some aspects of the presentdisclosure are identified herein as preferred or particularlyadvantageous, it is contemplated that the present disclosure is notnecessarily limited to these aspects.

It is noted that one or more of the following claims utilize the term“wherein” as a transitional phrase. For the purposes of defining thepresent inventive technology, it is noted that this term is introducedin the claims as an open-ended transitional phrase that is used tointroduce a recitation of a series of characteristics of the structureand should be interpreted in like manner as the more commonly usedopen-ended preamble term “comprising.”

What is claimed is:
 1. A multicore optical fiber comprising: a cladding,a plurality of waveguiding cores disposed in a cladding, wherein: theplurality of cores are situated adjacent to at least one other core witha core center to core center spacing being not larger than 10 times theradius of the average core, such that the greater than 10% of the lightwill couple from one core to the adjacent core over a propagatingdistance of 1 cm, along the fiber length so as to provide couplingbetween the adjacent cores and to enable quantum walk; and the pluralitywaveguiding cores are disposed in the cladding in a ring distribution orat least a portion of the ring distribution.
 2. A multicore opticalfiber according to claim 1, wherein said plurality of waveguiding coreshave the same propagation constant.
 3. A multicore optical fiberaccording to claim 1, wherein said plurality of waveguiding corescomprise at least two waveguiding cores with different propagationconstants.
 4. A multicore optical fiber comprising: a cladding, aplurality of cores disposed in a cladding, wherein: the plurality ofcores comprise one or more first waveguiding cores and one or moresecond waveguiding cores, wherein said cores are situated adjacent to atleast one other core with a core center to core center spacing being notlarger than 10 times the radius of the average core, such that thegreater than 10% of the light will couple from one core to the adjacentcore over a propagating distance of 1 cm, along the fiber length so asto provide coupling between the adjacent cores and to enable continuousquantum walk; the one or more first waveguiding cores comprise a firstpropagation constant, the one or more second waveguiding cores comprisea second propagation constant, and the first propagation constant isdifferent than the second propagation constant; and the one or morefirst waveguiding cores and the one or more second waveguiding cores aredisposed in the cladding in a ring distribution and at least a portionof the ring distribution is arranged based on a non-periodic or aquasi-periodic sequence.
 5. The multicore optical fiber according toclaim 4, wherein first propagation constant and the second propagationconstant are the same.
 6. The multicore optical fiber according to claim4, wherein first propagation constant and the second propagationconstant are the not the same.
 7. A multicore optical fiber comprising:a cladding, a plurality of cores disposed in a cladding, wherein: theplurality of cores comprise one or more first waveguiding cores and oneor more second waveguiding cores, wherein said cores are situatedadjacent to at least one other core with a core center to core centerspacing being not larger than 10 times the radius of the average core,so as to provide coupling between the adjacent cores to enablecontinuous quantum walk, such that the greater than 10% of the lightwill couple from one core to the adjacent core over a propagatingdistance of 1 cm, along the fiber length; the one or more firstwaveguiding cores comprise a first propagation constant, the one or moresecond waveguiding cores comprise a second propagation constant; and theone or more first waveguiding cores and the one or more secondwaveguiding cores are disposed in the cladding in a ring distributionand at least a portion of the ring distribution is arranged based on aperiodic sequence.
 8. The multicore optical fiber according to claim 7,wherein first propagation constant and the second propagation constantare the same.
 9. The multicore optical fiber according to claim 7,wherein first propagation constant and the second propagation constantare the not same.
 10. The multicore optical fiber of claim 1, wherein aspacing distance D between each adjacent pair of waveguiding cores inthe plurality of waveguiding cores comprises about 30 μm or less. 11.The multicore optical fiber of claim 7 wherein a spacing distance Dbetween each adjacent pair of waveguiding cores in the plurality ofwaveguiding cores is between 10 μm and 30 μm.
 12. A system comprising:the multicore optical fiber of claim 1; a photon generator opticallycoupled to an input end of at least one waveguiding core of theplurality of waveguiding cores; and one or more photon detectorsoptically coupled to an output end of at least one waveguiding cores ofthe plurality of cores.
 13. The system of claim 12, wherein said systemis a quantum communication system.
 14. The system of claim 12, whereinsaid system is a quantum computer system.
 15. A system comprising: themulticore optical fiber of claim 7; a photon generator optically coupledto an input end of at least one waveguiding core of the plurality ofwaveguiding cores; and one or more photon detectors optically coupled toan output end of at least one waveguiding cores of the plurality ofcores.
 16. The system of claim 15, wherein said system is a quantumcommunication system.
 17. The system of claim 15, wherein said system isa quantum computer system.